emE                  package:mclust                  R Documentation

_E_M _a_l_g_o_r_i_t_h_m _s_t_a_r_t_i_n_g _w_i_t_h _E-_s_t_e_p _f_o_r _a _p_a_r_a_m_e_t_e_r_i_z_e_d _M_V_N _m_i_x_t_u_r_e _m_o_d_e_l.

_D_e_s_c_r_i_p_t_i_o_n:

     Implements the EM algorithm for a parameterized MVN mixture model,
     starting with the expectation step.

_U_s_a_g_e:

     emE(data, mu, sigmasq, pro, eps, tol, itmax, equalPro, warnSingular,
         Vinv, ...)
     emV(data, mu, sigmasq, pro, eps, tol, itmax, equalPro, warnSingular,
         Vinv, ...)
     emEII(data, mu, sigmasq, pro, eps, tol, itmax, equalPro, warnSingular,
           Vinv, ...)
     emVII(data, mu, sigmasq, pro, eps, tol, itmax, equalPro, warnSingular,
           Vinv, ...)
     emEEI(data, mu, decomp, pro, eps, tol, itmax, equalPro, warnSingular,
           Vinv, ...)
     emVEI(data, mu, decomp, pro, eps, tol, itmax, equalPro, warnSingular,
           Vinv, ...)
     emEVI(data, mu, decomp, pro, eps, tol, itmax, equalPro, warnSingular,
           Vinv, ...)
     emVVI(data, mu, decomp, pro, eps, tol, itmax, equalPro, warnSingular,
           Vinv, ...)
     emEEE(data, mu, Sigma, pro, eps, tol, itmax, equalPro, warnSingular,
           Vinv, ...)
     emEEV(data, mu, decomp, pro, eps, tol, itmax, equalPro, warnSingular,
           Vinv, ...)
     emVEV(data, mu, decomp, pro, eps, tol, itmax, equalPro, warnSingular,
           Vinv, ...)
     emVVV(data, mu, sigma, pro, eps, tol, itmax, equalPro, warnSingular,
           Vinv, ...)

_A_r_g_u_m_e_n_t_s:

    data: A numeric vector, matrix, or data frame of observations.
          Categorical variables are not allowed. If a matrix or data
          frame, rows correspond to observations and columns correspond
          to variables. 

      mu: The mean for each component. If there is more than one
          component, 'mu' is a matrix whose columns are the means of
          the components.  

 sigmasq: for the one-dimensional models ("E", "V") and spherical
          models ("EII", "VII"). This is either a vector whose _k_th
          component is the variance for the _k_th component in the
          mixture model ("V" and "VII"), or a scalar giving the common
          variance for all components in the mixture model ("E" and
          "EII"). 

  decomp: for the diagonal models ("EEI", "VEI", "EVI", "VVI") and some
          ellipsoidal models ("EEV", "VEV"). This is a list described
          in more detail in 'cdens'. 

   Sigma: for the equal variance model "EEE". A _d_ by _d_ matrix
          giving the common covariance for all components of the
          mixture model. 

   sigma: for the unconstrained variance model "VVV". A _d_ by _d_ by
          _G_ matrix array whose  '[,,k]'th entry is the covariance
          matrix for the _k_th component of the mixture model. 

     ...: An argument giving the variance that takes one of the
          following forms:

          _d_e_c_o_m_p for models "VVV", "EII" and "VII"; see 'cdens'. 

          _c_h_o_l_S_i_g_m_a see Sigma, for "EEE".

          _c_h_o_l_s_i_g_m_a see sigma, for "VVV".

          _s_i_g_m_a see sigma, for "VVV".

          _S_i_g_m_a see Sigma, for "EEE".

               The form of the variance specification is the same as
               for the output for the 'em', 'me', or 'mstep' methods
               for the specified mixture model.

               Also used to catch unused arguments from a 'do.call'
               call.

     pro: Mixing proportions for the components of the mixture.  There
          should one more mixing proportion than the number of MVN
          components if the mixture model includes a  Poisson noise
          term. 

     eps: A scalar tolerance for deciding when to terminate
          computations due to computational singularity in covariances.
            Smaller values of 'eps' allow computations to proceed
          nearer to singularity.  The default is '.Mclust\$eps'. 

     tol: A scalar tolerance for relative convergence of the
          loglikelihood values.  The default is '.Mclust\$tol'. 

   itmax: An integer limit on the number of EM iterations.  The default
          is '.Mclust\$itmax'. 

equalPro: A logical value indicating whether or not the components in
          the model are  present in equal proportions. The default is
          '.Mclust\$equalPro'. 

warnSingular: A logical value indicating whether or not a warning
          should be issued whenever a singularity is encountered. The
          default is '.Mclust\$warnSingular'. 

    Vinv: An estimate of the reciprocal hypervolume of the data region.
          The default is determined by applying function  'hypvol' to
          the data. Used only when 'pro' includes an additional mixing
          proportion for a noise component. 

_D_e_t_a_i_l_s:

     This function can be used with an indirect or list call using
     'do.call', allowing the output of e.g. 'mstep' to be passed 
     without the need to specify individual parameters as arguments.

_V_a_l_u_e:

     A list including the following components:  

       z: A matrix whose '[i,k]'th entry is the conditional probability
          of the _i_th observation belonging to the _k_th component of
          the mixture.   

  loglik: The logliklihood for the data in the mixture model.  

      mu: A matrix whose kth column is the mean of the _k_th component
          of the mixture model. 

   sigma: For multidimensional models, a three dimensional array  in
          which the '[,,k]'th entry gives the the covariance for the
          _k_th group in the best model. <br> For one-dimensional
          models, either a scalar giving a common variance for the
          groups or a vector whose entries are the variances for each
          group in the best model. 

     pro: A vector whose _k_th component is the mixing proportion for
          the _k_th component of the mixture model. 

modelName: Character string identifying the model. 

             *  '"info"': Information on the iteration.

             *  '"warn"': An appropriate warning if problems are
                encountered in the computations.

_R_e_f_e_r_e_n_c_e_s:

     C. Fraley and A. E. Raftery (2002a). Model-based clustering,
     discriminant analysis, and density estimation. _Journal of the
     American Statistical Association 97:611-631_.  See <URL:
     http://www.stat.washington.edu/mclust>. 

     C. Fraley and A. E. Raftery (2002b). MCLUST:Software for
     model-based clustering, density estimation and  discriminant
     analysis.  Technical Report, Department of Statistics, University
     of Washington.  See <URL: http://www.stat.washington.edu/mclust>.

_S_e_e _A_l_s_o:

     'em', 'mstep', 'mclustOptions', 'do.call'

_E_x_a_m_p_l_e_s:

     data(iris)
     irisMatrix <- as.matrix(iris[,1:4])
     irisClass <- iris[,5]

     msEst <- mstepEEE(data = irisMatrix, z = unmap(irisClass))
     names(msEst)

     emEEE(data = irisMatrix, mu = msEst$mu, pro = msEst$pro,
     cholSigma = msEst$cholSigma)
     ## Not run: 
     do.call("emEEE", c(list(data=irisMatrix), msEst)) ## alternative call
     ## End(Not run)

